Answer on Mechanics | Relativity Question for Henry

2012-02-14T08:26:28-0500

Question #6508

A zookeeper finds an escaped monkey hanging from a light pole 4.5 meters high. Aiming her gun at the monkey, the zookeeper kneels 12.0 meters from the pole. The tip of her gun is .75 meter above the ground. the monkey tries to trick the zookeeper by dropping a banana, then continues to hold onto the pole. When the monkey releases the banana, the sookeeper shoots. If the bullet travels 45.0 m/s, will it hit the monkey, the banana, or neither one?

Expert's answer

2012-02-14T11:12:10-0500

T(of bullet riching bananaor monkey)=S/v=sqrt((4.5-0.75)2+122)/45=0.28 sBanana will drop by the time 0.28 sec at distanceD=g(t^2)/2 =9.8*(0.28^2)/2 =0.39mSo banana will be already droppen and the bullet hits the monkey.[img 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[/img]